The main types of electron energy distribution determined by model fitting to optical emissions during HF wave ionospheric modification experiments

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1 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, , doi: /jgra.50364, 2013 The main types of electron energy distribution determined by model fitting to optical emissions during HF wave ionospheric modification experiments M. N. Vlasov, 1 M. C. Kelley, 1 and D. L. Hysell 2 Received 21 March 2012; revised 30 April 2013; accepted 29 May 2013; published 25 June [1] Enhanced optical emissions observed during HF pumping are induced by electrons accelerated by high-power electromagnetic waves. Using measured emission intensities, the energy distribution of accelerated electrons can be inferred. Energy loss from the excitation of molecular nitrogen vibrational levels (the vibrational barrier) strongly influences the electron energy distribution (EED). In airglow calculations, compensation for electron depletion within the 2 3 ev energy range, induced by the vibrational barrier, can be achieved via electrons with an EED similar to a Gaussian distribution and energies higher than 3 ev. This EED has a peak within the 5 10 ev energy range. We show that the main EED features depend strongly on altitude and solar activity. An EED similar to a power law distribution can occur above km altitude. Below 270 km altitude, a Gaussian distribution for energies between 3 ev and 10 ev, together with a power law distribution for energies higher than 10 ev, is indicated. A Gaussian distribution combined with an exponential function is needed below 230 km altitude. The transition altitude from Gaussian to power law distribution depends strongly on solar activity, increasing for high solar activity. Electrons accelerated during the initial collisionless stage can inhibit the depletion of fast electrons within the vibrational barrier range, an effect that strongly depends on altitude and solar activity. The approach, based on the effective root square electric field, enables EED calculation, providing the observed red-line intensities for low and high solar activities. Citation: Vlasov, M. N., M. C. Kelley, and D. L. Hysell (2013), The main types of electron energy distribution determined by model fitting to optical emissions during HF wave ionospheric modification experiments, J. Geophys. Res. Space Physics, 118, , doi: /jgra Introduction [2] Increased intensities in optical emissions due to the impact of powerful electromagnetic waves (HF heating) on the ionospheric F 2 region have been observed many times [Haslett and Megill, 1974; Adeishvili et al., 1978; Djuth et al., 1987; Bernhardt et al., 1989, 1991]. The red (630.0 nm) and green (557.7 nm) line emissions of atomic oxygen are the main features of this artificial airglow. The excitation of these emissions requires fast electrons with energies above 1.96 ev and 4.19 ev, respectively. The first attempts to explain airglow excitation due to HF heating of ionospheric plasma showed that fast electrons corresponding to a Maxwellian electron energy distribution (MEED) with an appropriately elevated temperature can provide the 1 School of Electrical and Computer Engineering, Cornell University, Ithaca, New York, USA. 2 School of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York, USA. Corresponding author: M. C. Kelley, Cornell University, 318 Rhodes Hall, Ithaca, NY 14853, USA. (mck13@cornell.edu) American Geophysical Union. All Rights Reserved /13/ /jgra observed enhancements of red-line emissions [Mantas, 1994; Mantas and Carlson, 1996; Vlasov et al., 2005]. [3] Considering the observed enhancements of the red and green emissions excited by HF heating, Haslett and Megill [1974] concluded that a MEED could be used because of the unrealistically high electron temperature. Simultaneous radar observations of electron density and temperature and multistation optical observations of red-line enhancements [Gustavsson et al., 2001] showed significant deviations from the thermal model. The red-line emission intensity was only one third of the thermal model prediction, meaning that heating and electron acceleration by HF must also to be taken into account. [4] The necessity for a nonthermal component of the electron energy distribution (EED) is more obvious when analyzing the observed enhancements of red and green lines [Bernhardt et al., 1989]. Gustavsson et al. [2001] concluded that the enhanced airglow at nm and nm they observed during HF radio wave pumping in the F region could only be provided by a nonthermal electron population. [5] Vlasov et al. [2005] showed that, using a MEED with two electron temperatures (the observed temperature for thermal electrons and a much higher effective temperature for fast electrons with energies higher than 2 ev), explaining 3877

2 the observed enhancements of both emissions is difficult. They found that suprathermal electrons with an EED differing significantly from the MEED are needed to excite the observed red and green-line emissions. These fast electrons can be produced by Langmuir wave, upper hybrid wave, or Bernstein-mode wave acceleration in the region of the ionosphere where most of the HF radiation is absorbed [Gordon and Carlson, 1974; Meltz and Perkins, 1974; Gurevich et al., 1985; Newman et al., 1998; Gurevich et al., 2003]. For example, Wang et al. [1997] andnewman et al. [1998] showed that Langmuir turbulence near the critical height may produce suprathermal electrons with energies greater than 4.19 ev, the level necessary to excite atomic oxygen at 1 S states. More recently, Gurevich et al. [2003] discussed the importance of acceleration near the altitude where the heater frequency equals the upper hybrid frequency. This may explain the airglow enhancement that occurs when the heater beam is oriented in the magnetic zenith direction, as reported by Pedersen et al. [2003]. The observation by Gustavsson et al. [2005] of the emission radiated by N + 2 ions showed that the mechanism of electron acceleration can be complex. However, this problem is not the focus of this paper. [6] Wang et al. [1997] numerically solved the one-dimensional Vlasov equation for conditions appropriate to the ionospheric F region during HF-heating modification. They found that the EED of suprathermal electrons induced by HF heating can be close to a power law. Analyzing the intensities of the red and green lines observed within 10 s just after the start of HF heating, Mishin et al. [2004] found that the EED can be given by a power law function. This result is obtained by solving the kinetic equation for collisionless approximation and is in agreement with the results of Wang et al. [1997]. The results of Wang et al. [1997] and Mishin et al. [2004] correspond to the initial electron energy spectrum. Vlasov et al. [2005] analyzed High Frequency Active Auroral Research Program (HAARP) imager measurements and showed that, using the bi-maxwellian electron energy distribution (EED), it is impossible to obtain agreement between the calculated and measured intensities of the red and green lines because thermal electrons heated by suprathermal electrons additionally excite the red-line emission, whereas excitation of the green-line emission is negligible. However, this problem can be solved if the suprathermal electron distribution is modeled by a power law. This result means that a power law can also take place for the final EED, which is controlled by inelastic collisions. [7] Gustavsson et al. [2001] reported a red-line intensity enhancement that was much smaller than the enhancement they expected, based on thermal electrons using the measured electron temperature of 3500 K. They suggested that a strong depletion of electrons with energies higher than 2 ev took place because of electron energy loss due to the vibrational excitation of N 2. [8] The impact of N 2 vibrational excitation on the EED is also known. This effect was first observed and studied in N 2 discharges sustained by an electric field [Nighan, 1970]. A review of more recent results is presented in Capitelli et al. [2000]. According to these results, the EED decreases sharply in the energy range from 2 to 3 ev due to the excitation of N 2 vibrational levels. The excitation of these levels creates a sharp energy barrier that electrons must overcome to reach higher energies. The EED in this transitional region thus can deviate strongly from a Maxwellian distribution. [9] Both measurements and calculations of the photoelectron spectrum in the ionosphere also indicate the depletion of electrons with energies of 2 to 3 ev [Nagy and Banks, 1970; Mukai and Hirao, 1973]. However, the influence of this barrier on the depletion of photoelectrons with higher energies (e.g., above 4 ev) is insignificant because the photoelectron source in the ionosphere is very different from the source of fast electrons in a discharge. Calculations of EED, including the excitation of vibrational and electronic levels of neutral constituents corresponding to the E region, were carried out and reported in a set of papers [Vlasov et al., 1981; Dyatko et al., 1989; Milikh and Dimant, 2002]. A depletion of electrons with energies of around 2 ev was found, resulting from very effective vibrational excitation of N 2 in the background electron state. [10] First, Bernhardt et al. [1989] calculated the EED using a numerical model with the initial acceleration of electrons due to large-amplitude Langmuir waves and the impact of inelastic collisions on the initial EED. They included the influence of N 2 vibrational excitation (e-v collisions) on the energy distribution of the suprathermal electron flux in their model. However, they considered the results of HF heating at 300 km altitude for low solar activity when the N 2 density was very low. In this case, the frequency of electron-electron collisions is much higher than the frequency of e-v collisions, and the effect of N 2 vibrational excitation is negligible. [11] Mishin et al. [2000] attempted to estimate the influence of vibrational excitation on EED during HF modification of the F region. A significant deviation of the EED from a MEED was found. However, the authors concluded that this deviation occurs only during the initial moments because vibrationally excited molecules quickly return their excitation energy to electrons due to collisions of the second kind and to the EED approaches to the MEED. The authors estimated the relaxation time of the EED to MEED, t r = 1 min, and concluded that if the heating period exceeds t r,useofameedmaybejustified. If the period between HF pumping exceeds 1 min, the scenario repeats for each pulse; otherwise, the MEED should be used for each subsequent on-period. [12] Ignoring the energy transfer from vibrationally excited N 2 to electrons, Gustavsson et al. [2004] presented their estimates of EED depletion due to energy losses resulting from the vibrational excitation of N 2. They obtained a very deep depletion in the EED as compared with the results of Mishin et al. [2000]. However, the methods used by Gustavsson et al. [2004] in estimating the effects of e-v collisions and e-e collisions on the EED do not satisfy the main criterion for applying these methods. In general, this approach is not self-consistent, and only approximate estimates can be made. In their subsequent papers [Gustavsson et al., 2005; Gustavsson and Eliasson, 2008], the authors used the rough estimate of EED depletion given by the jump discontinuities function. [13] Vlasov et al. [2004] developed a theoretical model of the vibrational barrier based on analytical and numerical solutions of the Boltzmann equation for electron kinetics and an equation for vibrational kinetics. The EED obtained by Vlasov et al. [2004] is very different from the EED 3878

3 Figure 1. Cross sections for the O( 1 S) excitation calculated by formulas (1) and (2), curves 1 and 2, respectively. estimated by Mishin et al. [2000]. However, Vlasov et al. s [2004] main result is that the effect of collisions of the second kind is negligible because the time scale for this process is about, or longer than, 1 h instead of 1 min, as estimated by Mishin et al. [2000]. This important result means that the MEED cannot take place during HF heating. [14] The vibrational barrier model developed by Vlasov et al. [2004] facilitated explaining the very low intensity of the red-line emission observed by Gustavsson et al. [2001]. Also, Vlasov et al. [2004] showed that vibrational excitation of N 2 by suprathermal electrons could cause the observed saturation of red-line emissions during heater power increases. In their model, the saturation is induced by the electron density depletion due to the impact of N 2 vibrational excitation on recombination. The impact of the vibrational excitation on electron density during HF heating was considered first by Vlasov and Izakova [1990]. [15] Using data from emissions with wavelengths of 630.0, 557.7, 844.6, and nm, together with measurements of electron concentration and ion and electron temperatures, Gustavsson et al. [2005] estimated the EED during HF heating. The authors used a simplified approach that takes into account the effect of the vibrational barrier on the EED. They sharply cut the population of electrons with energy equal to 2 ev, assuming depletion between 10% and 90% in the EED. According to the authors estimates, the EED for energies above 2 ev and below 15 ev may often be thermal-like with temperatures between 9000 and K. Also, they found that the EED is flat for an accelerated component with energies from 15 to 50 ev. [16] The goal of this paper is to estimate the EED of suprathermal electrons induced by HF heating at different altitudes. These estimates are based on the well-known relation between the emission intensity excited by electron impact and the flux of suprathermal electrons. Using new [Hysell et al., 2012] and previously published emission data, together with a model of the vibrational barrier and the electron kinetics behind this barrier, we infer the EED formed at different altitudes and under different geophysical conditions. The main features of these EED are very different from the previous EED estimated by Bernhardt et al. [1989], Gustavsson et al. [2005], and Gustavsson and Eliasson [2008]. 2. Analysis of Experimental Data on the Cross Sections and Coefficients for Excitation of the 1 S, 1 D, and 3p 3 P States of Atomic Oxygen [17] We begin analyzing the cross sections of electron inelastic collisions with atomic oxygen because the emission intensities used by us for EED determination depend directly on this parameter O( 1 S) [18] The widely used cross-section approximation for the O( 1 S) excitation measured by Doering and Gulcicek [1989] is given by the formula ðe th EÞ s 1 ðeþ ¼ AE ð E th Þexp ; (1) ðe m E th Þ with A = , E th = 4.19 ev, and E m = 10 ev. Majeed and Strickland [1997, hereinafter MS-1997] reanalyzed the cross-sectional data and tabulated cross sections in good agreement with the measurements. These cross sections can be approximated by the formula s 2 ðeþ ¼ AE ð E th Þ g ðe th EÞ exp ; (2) ðe m E th Þ with parameters A = , g = 0.82, and E m = 16 ev. The cross sections calculated with formulas (1) and (2) are shown in Figure 1. Using the cross section and electron energy distribution, the rate coefficient of the O( 1 S) excitation can be calculated using the formula k 1S ¼ Z 1 Eth sðeþð2e=m e Þ 1=2 fðeþde; (3) where m e is the electron mass and f(e) is the electron energy distribution. The rate coefficient for the O( 1 S) excitation calculated with the cross section given by formulas (1) and (2) and the MEED are very close. Also, as seen from Table 1, there is good agreement between the k 1S value with the cross sections given by formula (2) and k 1S calculated by the formula k 1S ¼ A ðt e =0:0861Þ y expð E=T e Þ; (4) where A = 1.75, g = 0.318, and E = 4.19 ev, as given by Capitelli et al. [2000]. Note that the cross section recommended by Capitelli et al. [2000] is h s C ðeþ ¼ Að1 E th =EÞexp P 4 k¼0 b k ðlne with b 0 = 0.147, b 1 = 0.389, b 2 = , b 3 = 0.271, and b 4 = , strongly contradicting their formula (3). For example, the k 1S maximum value calculated with the Table 1. Rate Coefficients for the Excitation of O( 1 S) Atoms T e (K) k1s (cm 3 s 1 ) MEED PLEED b GM-1997 a Our model Capitelli s 1 s 2 with s 1 et al a Gurevich and Milikh [1997]. b PLEED: power law EED. Þ k i ; (5) 3879

4 Figure 2. Cross sections for the O( 1 D) excitations given by formula (1) with parameters A = 3.5e -17, E th = 1.96 ev, and E m = 6 ev (dashed curve) and given by the good approximation of data presented by Majeed and Strickland [1997] (solid curve). cross section given by formula (5) is equal to cm 3 /s for T e = 3000 K, but the k 1S value calculated by formula (4) is equal to cm 3 /s (see Table 1). The difference between the k 1S values calculated with cross sections s 1 and s 2 given by formulas (1) and (2), respectively, is very significant for the electron energy distribution corresponding to a power law (PLEED) (see Table 1). These calculations were made with the power law distribution normalized to the MEED for an energy of 3 ev. Note that the cross sections used by Gustavsson et al. [2005] and based on the data presented by Itikawa and Ichimura [1990] are much larger than the cross sections given by MS-1997 for energies higher than 45 ev. The ratio of these cross sections is 4.6 for E = 100 ev. This difference is important for the rate coefficient calculated for electron energy distributions given by the power law for energies higher than a few electron volts or any distribution that significantly exceeds the MEED for these energies O( 1 D) [19] The data on cross sections for the O( 1 D) excitation tabulated by MS-1997 can be approximated by the formulas: h i n o s MS ¼ A 1 ðe 1:96Þ 0:8 exp ½ðE 1:96Þ=4:5Š 0:9 for 1:96 ev E 20 ev; (6a) s MS ¼ A 2 expð 0:0507EÞ for 20 ev E 50 ev; (6b) s MS ¼ A 3 expð 0:025EÞ for 20 ev E 50 ev; (6c) where A 1 = , A 2 = ,andA 3 = As seen from Figure 2, the cross sections for the O( 1 D) excitation corresponding to the approximation of the cross sections tabulated in MS-1997 are larger than the cross sections calculated by formula (1) with parameters A = , E th = 1.96 ev, and E m = 6 ev. This difference leads to significant differences between the k 1D values calculated for the MEED. As seen from Table 2 (column MS-97), the k 1D values calculated with the cross sections given by formulas (6a) (6c) are higher by a factor of about 2.3 than the k 1D values calculated by formulas recommended by Capitelli et al. [2000] and Mantas and Carlson [1996]. Also, the k 1D values in column MS are higher than the k 1D values calculated with cross sections given by formula (1) (column M1). However, the power law distribution, which can be assumed for energies higher than 3 ev, does not significantly change the k 1D values. Note that the cross sections used by Gustavsson et al. [2005] and based on the data presented by Itikawa and Ichimura [1990] and Itikawa et al. [1986] are much larger than the cross sections given by MS-1997 for energies higher than 30 ev. The ratio of these cross sections is 6 for an energy of 100 ev. These high cross sections used by Gustavsson et al. [2005]can influence the rate coefficient calculated for electron energy distributions given by the power law at energies higher than a few electron volts or any distribution that significantly exceeds the MEED at these energies O(3p 3 P) [20] The cross section for the excitation of the nm emission tabulated by MS-1997 can be approximated by the formula sðeþ ¼ AE ð 10Þ 1:3 exp½ðe 15Þ=10Š for E 10 ev (7) with A = The rate coefficient corresponding to this cross section is very small for the MEED but can be strongly increased by the power law distribution. In any case, this emission can only be observed if a portion of the electrons with E > 10 ev is much higher than the portion of these electrons corresponding to the MEED. Note that the cross sections recommended by Capitelli et al. [2000] are smaller by a factor of 35 than the s values given by formula (7). 3. Conditions for Nighttime Background EED in the F Region [21] Our analysis of the original ionospheric conditions starts from an altitude of 210 km. We consider the conditions for the night of 9 November 2010 because new optical data were obtained under these conditions [Hysell et al., 2012]. [22] The ionospheric plasma is strongly ionized when the collision frequency of electrons with electrons, υ ee, is much higher than the frequency of electron elastic collisions with neutrals, υ en, multiplied by the mean relative electron energy loss in these collisions, d el =2m e /M n, where m e and M n are Table 2. Rate Coefficients for the Excitation of O( 1 D) Atoms T i (K) k 1D (cm 3 s 1 ) MEED MC-1996 a M1 Capitelli et al. MS a Mantas and Carlson [1996]. 3880

5 in neutral density. The very large cross section for vibrational excitation, s ev, due to inelastic collisions of molecular nitrogen with electrons having energy in the range of 2 3 ev can result in significant deviation of the EED from the MEED because, in this case, the e-v collision frequency, given by the formula υ ev ¼ s ev E 1=2 ½N 2 Š; (10) is larger than the υ ee value, as seen from Figure 3a. A significant depletion of initially accelerated electrons can be produced by energy loss from vibrational excitation. However, this depletion cannot exist for a long time due to collisions of the second kind, which transport energy from vibrationally excited nitrogen to electrons (V e exchange) and reconstruct the MEED. The relaxation time from the depleted EED to the MEED is estimated to be about a few hours at 210 km. This time depends on the rate of energy exchange between the vibrational and translational degrees of freedom (V-T exchange) provided by collisions of vibrationally excited N 2 with atomic oxygen. Note that the MEED would exist if a Boltzmann distribution of the population of N 2 vibrational levels could be maintained. However, the anharmonism of N 2 induces an additional population of high vibrational levels that influences the EED. The populations of N 2 vibrational levels corresponding to the anharmonic model in ionospheric plasma were investigated in detail by Vlasov and Smirnova [1995], who showed that a large enhancement of the population of vibrational levels higher than the seventh level can occur, inducing a significant deviation of the EED from the MEED for energies within the range of 2 3 ev. [23] The frequency of inelastic collisions of electrons with atomic oxygen is given by the formula υ eo ¼ s MS E 1=2 ½OŠ; (11) Figure 3. (a) The frequency of inelastic collisions of electrons with molecular nitrogen (curve 1), atomic oxygen for the production of O( 1 D) (curve 2), and the frequency of electron-electron collisions, N e = cm 3 at 210 km (curve 3). (b) Collision frequencies of electrons with electrons (dashed curve) and for the N 2 vibrational excitation (solid curve) and the O( 1 D) excitation (dashed-dotted curve) at 250 km. the electron and neutral masses, respectively. The d el value is equal to at 210 km. Using the formulas υ ee ¼ 1: N e E 1:5 and (8) υ en ¼ N n E 1=2 ; (9) it is possible to estimate υ ee = 8.6 s 1 and υ en = 0.36 s 1 for E = 1.9 ev, N e = cm 3, and N n = cm 3 at 210 km. Here and further on, we used the MSIS-E-90 model of the neutral densities [Hedin, 1991]. Taking into account the small d el value, the d el υ en value is much less than the υ ee value for any low electron density. This result means that the electron-electron collisions dominate for energies less than 2 ev, and in this case, the ionospheric plasma is strongly ionized, and the EED corresponds to the MEED. Note that the MEED also occurs above 210 km because of the decrease where the υ eo value of 16 s 1 can be estimated for E =4eV and [O] = cm 3 at 210 km. This collision frequency is larger than the frequency of electron-electron collisions, υ ee = 2.8 s 1. As seen from Figure 3a, these inelastic collisions dominate, and a strong difference between the EED and the MEED should exist for energies higher than 3 ev. The O( 1 D) atoms are produced as a result of these collisions. Energy transport from these excited atoms to electrons, owing to collisions of the second kind, is impossible because of the fast quenching of O( 1 D) atoms by collisions with neutrals and radiation. [24] Note that secondary electrons produced by ionization of O atoms by electrons with energies higher than 20 ev can increase the population of electrons with energies less than 10 ev, but this effect is very small and cannot compensate the energy loss caused by excitation of the lower electronic states of atomic oxygen. Unfortunately, calculations of the EED formed by inelastic collisions are very complicated, but in any case, the nighttime background EED is very different from the MEED for energies higher than 3 ev for N e = cm 3 at 210 km under the geophysical conditions of 9 November [25] Comparing the collision frequencies shown in Figures 3a and 3b, the impact of inelastic collisions on the EED discussed above depends on the altitude because of the decrease in neutral density with increasing altitude. For example, the same υ eo /υ ee ratio as at an altitude of 210 km 3881

6 for an energy of 4 ev can be obtained for the energy of 8 ev at 300 km altitude, meaning that a strong depletion of accelerated electrons can only occur for energies higher than 8 ev at 300 km. Thus, the production of fast electrons accelerated by the interaction of electromagnetic waves with ionospheric plasma should be more effective at higher altitudes. Also, the increase in electron density can decrease the impact of inelastic collisions on the EED. However, this strongly depends on specific features of the interaction between the waves and the ionospheric plasma. 4. Estimates of the EED During Ionospheric Modification by Power Electromagnetic Waves 4.1. Approach for EED Derivation From Optical Emissions [26] First, we use the data obtained from ionospheric modification experiments performed on 9 November 2010 at the HAARP facility (18.6 N, 66.7 W) in Alaska [Hysell et al., 2012]. The experiments involved continuous wave heating at full HAARP power in the direction of magnetic zenith. Heating occurred from , , , , and UT. The pump frequency was 3.4 MHz before 0330 UT and 2.85 MHz thereafter. A description of the HAARP spectrometer and calibration of the data are presented in Hysell et al. [2012]. The data show clear background red- and green-line emissions as well as heater-induced red- and green-line enhancements and the emission at nm with intensities 77.9, 34.4, and 21.7 R, respectively. [27] In our analyses, we will use the 20 km figure for Δz for all emissions and assume a representative emission height of 210 km when estimating neutral densities as used in Hysell et al. [2012]. According to MSIS-E-90, the number densities of O and N 2 at 210 km would have been and cm 3 during the experiments at 4 UT with a neutral temperature of 723 K. Finally, using the rate coefficients for quenching given in Vlasov et al. [2005], we can use an estimate of 16.6 s for the lifetime of the O( 1 D) state at 210 km at night based on the MSIS-E-90 model for the time and altitude in question. [28] The column intensity of the emission corresponding to the radiative deactivation of the ith state excited by electron impact on the jth neutral constituent can be calculated using the well-known formula, 1 I ij ¼ 10 6 C ij N j ΔzZ v e ðeþs ij ðeþfðeþde; (12) Eth where I ij is the intensity in Rayleighs, C ij is the ratio of the Einstein coefficient to the total deactivation frequency of the ith state, N j is the density of the jth neutral constituent, Δz is the vertical thickness of the emission layer, v e is the electron velocity, s j is the cross section for the excitation of the ith state of the jth neutral constituent, and f (E) is the EED. Using equation (12), spectrometry data on the redand green-line emissions and the nm emission discussed above, together with the cross sections discussed in section 2, it is possible to infer the EED. [29] The T e in the heated area is uncertain in the HAARP experiments but, based on Arecibo observations, we believe that this temperature likely did not exceed 2500 K. At such T e, the intensity of the red line excited by thermal electrons would not exceed 9 R, so suprathermal electrons are necessary. If T e were as high as 3500 K [Hysell et al., 2012], thermal electrons could cause the observed red-line intensity. However, even in this case, the green-line intensity observed concurrently in these data could only be caused by suprathermal electrons. The combination of high T e and suprathermal electrons excite the red-line emission so, in such a case, the total red-line intensity would be much larger than the observed intensity. Taken together, the airglow data argue that the electron temperature should be significantly less than 3500 K and that suprathermal electrons are necessary to explain the data Discussion of Electron Energy Distribution Functions [30] The mechanism responsible for electron acceleration in ionospheric modification experiments remains unsettled. It is assumed that the increase in the suprathermal electron population can be induced due to stochastic and resonance interaction of plasma with turbulence produced by HF heating waves. The commonly used mechanism is that electrons are most efficiently accelerated by Langmuir turbulence (LT) generated in the radio wave interaction in the upper hybrid resonance region. Field-aligned density cavities generated in the heating area due to plasma outflow from this area play an important role. In any case, electrons are accelerated by high-frequency electric fields, and importantly, this frequency is much higher than the electron-neutral collision frequency in the F region. Electrons can pass the cavities many times due to elastic collision scattering because the cavity size is much less than the electron free path. Also, the strong effect of double resonance conditions on airglow suggests that other mechanisms may be involved [Djuth et al., 2005; Mishin et al., 2005; Kosch et al., 2005, 2007]. Detailed descriptions of the different mechanisms and additional references are presented in the review by Gurevich [2007]. We will return to this problem and consider the source function for accelerated electrons in sections 4.4 and 4.5. [31] Comprehensive experimental and theoretical investigations exist of the EED in atmospheric gas discharges sustained by high-frequency electric fields. Typical results in atmospheric gas (N 2 ) discharge show that the EED decreases sharply in the energy range of ~1.6 to ~ 3.5 ev due to excitation of electron ground-state vibrational levels. The EED in molecular oxygen does not exhibit the same vibrational barrier effects as in nitrogen. The population of accelerated electrons slowly decreases behind the barrier. Thus, these results show that the EED in N 2 or in atmospheric gas with high density N 2 is very different from the MEED. The impossibility of MEED use for the EED during HF heating was discussed in section 1. [32] It was shown above that the υ ev frequency is significantly higher than υ ee at 210 km, and the vibrational barrier effect on the EED is very strong. Using the model of the vibrational barrier [Vlasov et al., 2004], it is possible to calculate the EED within the energy range of ev. The population of accelerated electrons behind the barrier E = 3 ev can be found to be very low, f (E) = 0.3 cm 3 ev 1. If the EED behind the barrier is flat, the intensity of the red line cannot exceed 3.2 R, which is much less than the 3882

7 Table 3. Rate Coefficients for the Vibrational Excitation of N 2, K N2v T e (K) BK-1973 (cm 3 s 1 ) MS-97 (cm 3 s 1 ) observed intensity. This means that the electron energy distribution function should be the maximum for energies higher than 3 ev. However, this increase cannot extend to high energies because the total number of accelerated electrons is limited and the population of energetic electrons is f (E)! 0 for E!1. [33] The threshold of the O( 1 D) excitation coincides with the threshold of the vibrational barrier. The maximum ratio of υ ev = s V v e [N 2 ]toυ ee = N e E 1.5 is 11.6 for N e = cm 3 at 210 km (see also Figure 3a). In this case, we used the cross section for the N 2 vibrational excitation with the s V peak value of cm 2. MS-1997 recommends s V with the peak value equal to cm 2, and Campbell et al. [2004] recommend s V with the peak value equal to cm 2. From Table 3, the rate coefficient for the N 2 vibrational excitation by electrons with the MEED calculated with this s V corresponding to MS-1997 is larger by a factor of 2 than the usually used rate coefficients given by Banks and Kockarts [1973]. Comparing the k N2v values with the k 1D values given in Table 2, we conclude that the probability of N 2 vibrational excitation is much higher than the probability of O( 1 D) excitation at any electron temperature. [34] The rate coefficient for exciting green-line emissions for T e 3500 K cannot exceed cm 3 /s (see Table 1), and the green-line intensity excited by thermal electrons is very small. This means that the green-line emission observed in the modified ionosphere requires a very large electron enhancement for E > 4.19 ev and that the red- and green-line emissions observed in our case may require an EED that is very different from the MEED. on 9 November Note that the experimental data used to estimate the EED correspond to low solar activity. [36] To estimate the influence of electron transport on the EED inferred from the airglow, equations of continuity given by Banks and Nagy [1970] and Banks and Kockarts [1973] can be used for the upward F and downward P fluxes of suprathermal electrons. Bernhardt et al. [1989] and Gustavsson and Eliasson [2008] used this approach and investigated this problem in detail. We consider the transport influence on the EED to compare the influence of transport on the main features of the EED at different altitudes. First, we must estimate this effect on the EED peak shown in Figure 4a. We use the equations < cosy ¼ AF þ BP þ ð Þ < cosy > þqf and (13) < where ¼ AF þ BP þ ð q=2 Þ < cosy > þqp ; (14) 4.3. The EED Inferred From Emission Data Presented in Section 4.1 [35] We must start from the threshold of the O( 1 D) excitation corresponding to 1.96 ev that coincides with the vibrational barrier s initial energy. Using the vibrational barrier model developed by Vlasov et al. [2004], the EED can be obtained within the energy range of 2 3 ev. This EED and the MEED calculated for T e = 2000 K at 210 km are shown in Figure 4a. There is significant depletion of the electron population for energies higher than 1.6 ev. As a result of this depletion, a strong enhancement of the suprathermal electron population behind the vibrational barrier is necessary to provide the observed enhancement of the emissions. Our calculations show that the EED shown in Figure 4b and given by the Gaussian function for 3 ev E 10 ev and two exponential functions for 10 ev E 20 ev and 20 ev E 50 ev can provide the intensities I R =75.8R, I G =36R, and I = 18.8 R. Taking into account the uncertainty in the cross sections and in the neutral model, our results are in excellent agreement with the observations in the heated area at 210 km Figure 4. (a) The EED corresponding to I R = 75.8 R, I G = 36 R, and I = 18.8 R. (b) The EED for the same conditions as in Figure 4a but for 1.6 ev E 50 ev. 3883

8 Figure 5. The EED inferred from HAARP emission data I R = 125 R and I G = 12.5 R observed at 05:00 UT, 2 February 2002 at 260 km, with T e = 3000 K. A ¼ X k B ¼ X k n k s k in þ p els k el ; n k p el s k el ; F and P are the upward and downward fluxes, respectively, q is the source of suprathermal electrons, q is the suprathermal electron production due to cascading from higher energy electrons undergoing inelastic collisions, s k in and s k el are the cross sections for inelastic and elastic collision with the k-species, respectively, and p el = 0.5 is the backscattering probability for elastic collisions. Equations (13) and (14) do not include losses due to the energy transfer to ambient electrons used by Gustavsson and Eliasson [2008] because we use the Boltzmann equation solution for the EED calculation within the energy range of ev, according to Vlasov et al. [2004]. The electron-electron collisions are not important for energies higher than 3.5 ev, as seen from Figures 3a and 3b. The inelastic collisions of Figure 7. The EED given by Gustavsson et al. [2005] (curve 1), the EED inferred by us from the data on optical emissions used by Gustavsson et al. [2005] (curve 2), and the EED corresponding to the electron flux energy distribution presented by Gustavsson and Eliasson [2008]. electrons with atomic oxygen dominate within the energy range of ev where the peak of the EED occurs. The atomic oxygen is the main constituent at 210 km, and the N 2 density does not exceed 30% according to the MSIS-E- 90 model data on 9 November In this case, we can use atomic oxygen density in our approximate estimation. [37] The fluxes corresponding to the EED shown in Figure 4a can be used as the low boundary condition instead of the source function of energetic electrons. Using the variable quantity y = exp( z/h) instead of s = z sini and the equation produced by differentiation of the equation corresponding to the sum of equations (13) and (14) and by substituting the difference between equations (13) and (14) in the equation for the secondary derivative, it is possible to obtain the equation < 2 ðf þ PÞ ¼ H 2 n 2 0 s2 in þ 2s els in ðf þ PÞ; (15) where y=exp( z/h), H is the scale height, and z=s sini where I is the dip angle. The solution of equation (15) is given by the formula ðf þ P h Þ ¼ C l sinh Hn 0 s 2 in þ 2s i 1=2y els in h þ C 2 cosh Hn 0 s 2 in þ 2s 1=2y i els in : (16) Figure 6. The EED inferred from airglow observed at 210 km and shown in Figure 8 and calculated at other altitudes. [38] The C 1 and C 2 values can be determined by the boundary conditions. The fluxes corresponding to the EED shown in Figure 4a are used as the low boundary condition = 0 as the upper boundary condition. Using formula (16), the fluxes and EED can be calculated at different altitudes. As seen from the results shown in Figure 5, the EED corresponding to fluxes calculated by solution (16) strongly decreases with increasing altitude, but the shape of the EED changes insignificantly. 3884

9 Figure 8. The EED inferred from HAARP emission data I R =125R and I G = 12.5 R observed at 05:00 UT, 2 February 2002 at 260 km, with T e =3000K. [39] Using fluxes corresponding to the EED shown in Figure 5 as the lower boundary condition for solution (16), the EED can be calculated at altitudes above the heating located at around 260 km, as shown in Figure 6. In this case, the EED shape significantly changes and then the EED strongly decreases. This result strongly depends on solar activity. [40] The cascading effect can be estimated using the balance equation for the populations of energetic electrons with energy E [Schunk and Nagy, 2009]. This balance between the production of these electrons is due to the energy loss ΔE of electrons with energy E+ΔE and the loss of these electrons due to inelastic collision. Our estimate shows that the population increase can occur within the energy range of ev and that this increase does not exceed 10% because the inelastic energy losses within the energy range of 5 15 ev are much higher than the losses for energy larger than 15 ev The EED Inferred From Emission Data Under High Solar Activity [41] In Figure 7, we first consider the EED inferred by Gustavsson et al. [2005] from their emission data. We then infer the EED, also shown in Figure 7, corresponding to the same emission data, i.e., the intensities of 38, 9.8, and 8.14 R for the red, green, and nm emissions, respectively, which are very close to the intensities of 40, 10, and 8 R used by Gustavsson et al. [2005]. The shape of this EED differs significantly from the EED estimated by Gustavsson et al. [2005]. The main differences are the following: a deeper depletion within the energy range of 2 3eV and a maximum at 8 ev. The main cause of these differences is use of the vibrational barrier model in our calculations instead of the rough estimate made by Gustavsson et al. [2005]. Our calculated EED is described by a smooth continuous function, but the EED estimated by Gustavsson et al. [2005] corresponds to a discontinuous function for different parts of the EED. As seen from Figure 7, there is a strong difference between populations calculated by us and by Gustavsson et al. [2005]. According to our estimate, the red-line intensity corresponding to the EED inferred by Gustavsson et al. [2005] is larger by a factor of 30 than the intensity measured and used in this paper to estimate the EED. The Gustavsson et al. intensity exceeds 1 kr and is an unrealistic value because this nighttime intensity was never observed. Also, a large difference exists between the EED of Gustavsson et al. [2005] and the EED of Gustavsson and Eliasson [2008], shown in Figure 7. [42] Finally, our analysis shows that the EED at low altitudes is characterized by a strong depletion of the electron population induced by the vibrational barrier within the energy range of 2 3 ev, a significant maximum of the electron population in the range of 6 8 ev (corresponding to a Gaussian function peak within the range of 2 10 ev) and an exponential decrease in the population for energies higher than 10 ev. [43] Using HAARP data on the red- and green-line emissions given in Table 1 in Vlasov et al. [2005], it is possible Figure 9. The MEED for T e = 3000 K and N e = cm 3 (curve 1) and the EED inferred from the HAARP data (curve 2) on the red- and green-line intensities of 290 R and 48.3 R, respectively, observed at 08:30 UT on 5 February 2002 at 300 km. Figure 10. Height profiles of the energetic electron free path on 13 February and 9 November 2002 (solid and dasheddotted curves, respectively) for high solar activity and on 9 November 2009 (dashed curve) for lower solar activity. 3885

10 Table 4. Differing Parameters and Intensities of Red- and Green-Line Emissions Measured by HAARP During HF Heating in February 2002 [Vlasov et al., 2005] Measurement a Date f p (MHz) h p (km) N e (cm 3 ) I R (R) I G (R) I R /I G 1 02/ UT /09/ UT /13/ UT /13/ UT /17/ UT /17/ UT a 1, conical scan 15 off-zenith; 2 6, magnetic zenith. to estimate the EED at altitudes from 260 to 330 km. The EED inferred from the intensities I R = 125 R and I G = 12.5 R observed at 260 km is shown in Figure 8. In this case, the depletion of the electron population due to the vibrational barrier within the energy range of 2 3 ev at 260 km is significantly less than the depletion at 210 km because of the [N 2 ] decrease and the N e increase. However, the main difference of this EED from the EED at 210 km is the power law distribution of the electron population for energies higher than 10 ev at 260 km versus an exponential function used for 210 km. The electron population depletion induced by the vibrational barrier and the O( 1 D) deactivation decreases with increasing altitude, and the electron population enhancement within the energy range of 3 10 ev, needed to excite the redline emission, decreases. In this case, the green-line excitation requires a more sloping EED for E > 10 ev than can be approximated by the function, similar to the power law. [44] The EED corresponding to the intensities I R = 260 R and I G = 48.3 R observed at 300 km [Vlasov et al., 2005, Table 1] from the emission layer with a thickness of 20 km is shown in Figure 9. In this case, it is not necessary to have a peak in the electron population for E > 3 ev because of the low depletion of the electron population in the vibrational barrier and the deactivation of the O( 1 D) atoms, and a power law can be used. A similar EED can be inferred from the emission intensities observed at 330 km. We will discuss this problem further in section 4.5. [45] Unfortunately, data for the emission are not available, and uncertainty exists in the estimated EED for energies higher than 30 ev. If the intensity of this emission did not exceed a few Rayleighs, an exponential decrease in the EED would be needed The EED at Different Altitudes and for Low and High Solar Activities [46] The thickness of the LT layer in altitude is much smaller than the electron mean free path. This thickness is usually estimated to be m [Gurevich et al., 2004], and the free path is larger than 2 km at altitudes above 200 km, as seen from Figure 10. This means that the electron acceleration inside the LT layer is collisionless. This acceleration produces an EED of the initial electrons, which then lose their energy because of inelastic collisions with neutrals, and the final EED is formed. Gurevich et al. [2004] considered the collisionless acceleration of electrons and obtained a MEED with the effective electron temperature of T eff =5 10 ev. [47] Wang et al. [1997] obtained the electron velocity distribution (EVD), f (v e )= (32/v e ) 1.9, where the numerical solution of the Vlasov equation results in v e = V e / V Te and V Te =(T e /m e ) 1/2. The EED corresponding to this EVD can be given by the relation (T e /e) 0.85 as a power law. It can be assumed that an EED corresponding to a power law may occur after inelastic collisions and can provide the intensity of the red line observed at 210 km under low solar activity (9 November 2009), in this case, the EED given by the relation f ðþ¼ e N 0 ðt e =eþ 0:85 ; (17) N 0 =56cm 3 ev 1. However, energetic electrons with this EED produce a green-line intensity that is larger by a factor of 2.6 than the observed intensity. Also, the intensity of the emission is much higher than the observed value, meaning that the EED given by a power law obtained during the initial collisionless stage must be significantly changed due to inelastic collisions at low altitude and for low solar activity. The main cause of this phenomenon is very effective inelastic collisions with molecular nitrogen, accompanied by excitation of the vibrational levels. [48] We now apply the EED given by the power law to the red- and green-line emissions given in Table 4 that were observed under high solar activity. The EED given by a power law and normalized to the red-line intensity observed at 260 km on 13 February 2002 excites the green-line intensity, which is larger by a factor of 5.6 than the observed intensity. However, the EED given by the power law and normalized to the red-line intensity of 230 R observed at 270 km on 13 February 2002 can provide the green-line intensity shown in Table 4 for the case of ionospheric modification. In the HF heating case on 17 February 2002, at 330 km with the EED normalized to the red-line intensity of 230 R, the green line with an intensity of 46 R instead of the observed intensity Figure 11. EED calculated by the vibrational barrier model (solid curve), the EED numerically calculated by the model with the initial EED given by the power law [Wang et al., 1997], and inelastic collisions with N 2 for two different electron accelerations, t =310 4 s and s (dasheddotted and dashed curves, respectively), during the initial collisionless stage; the EED calculated by the analytical solution of the kinetic equation with e-e, e-v collisions; and the source function corresponding to EED produced during the initial collisionless stage (dotted curve). 3886

11 Figure 12. The n ev /n ee ratios at altitudes of 260, 270, and 280 km (solid, dashed, and dotted curves, respectively, for the experimental data given in Table 4. of 32.8 R can be obtained with the power law given by the formula f(e) = (T e /e) 1.2. In the other cases shown in Table 4, the green-line intensities calculated with the EED normalized to red-line intensities are much larger than the observed intensities. These results show that the EED calculated in the initial collisionless stage should be strongly changed due to inelastic collisions and cannot be presented by a power law in many cases for high solar activity. [49] We now consider EED produced within the energy range of the vibrational barrier (1.6 ev e 4 ev) with the source function corresponding to the EED given by the power law calculated by Wang et al. [1997] for the collisionless stage. The numerical solution results of the balance equation for energetic electrons are shown in Figure 11 (dashed and dashed-dotted curves). Two different EED correspond to the different intensities of the source function that depends on different durations of the electron acceleration for the initial stage. [50] The EED given by the power law can be approximated by the exponential function within the small energy range of ev. In this case, the analytical solution for the kinetic equation can be obtained by (" f ðþ¼c e 1 exp 1 1 2T e 4T 2 þ 0:5R # ) 1=2 ðe e 0 Þ e T e e av C 2 exp½ bðe e 0 ÞŠ; (18) where C 1 + C 2 = f 0 for e = e 0, C 2 = q 0 /[b 2 b/t e 0.5R/ (T e e av )], q 0 = N 0 A/t, A = , b = 0.33 ev 1, and R = n ev /n ee. [51] The EED calculated by this solution and normalized to f (e = 1.6 ev) given by the vibrational barrier model is shown by the dotted curve in Figure 11. If we could use the EED corresponding to the initially accelerated electrons as the source function, the energetic electron depletion within the vibrational barrier would decrease. However, the initial EED given by Wang et al. [1997] should increase by a factor of about 7. [52] It was demonstrated in section 2 that deviation of the EED from the MEED depends on the ratio υ ee /υ ev for energies of 2 3eV and the ratio υ ee /υ eo for energies of 3 20 ev. The depletion of energetic electrons within the vibrational barrier depends on the n ev /n ee ratio. These ratios, calculated at 260 and 270 km for the experimental data on 13 February 2002 and given in Table 4, are shown in Figure 12 (solid and dashed curves, respectively). [53] Taking into account that the ratio of the peak barrier values at 260 and 270 km is equal to 1.66 and the O( 1 D) quenching rate at 270 km is smaller by a factor of 1.14 than this rate at 260 km, the large difference between the intensities observed at this altitude is in excellent agreement with the differences of the barrier values and the quenching rates at these altitudes. Also, the differences between the red-line emission intensities observed at 280 and 270 km are in good agreement with the barrier value increase at 280 km and the decrease in the quenching rate at this altitude with respect to the parameters at 270 km. Thus, our consideration shows that a decrease in the vibrational barrier effect due to electrons accelerated before collisions is not significant. [54] Vibrational barriers differ strongly under low and high solar activity. Using the IRI-2007 and MSIS-E-90 models, the n ev /n ee ratio can be calculated at different altitudes for low and high solar activity. As seen from Figure 13, the higher barrier occurs for high solar activity. However, a decreasing barrier with increasing altitude is stronger for high solar activity than for low solar activity. The main cause of this difference is the sharp increase in electron density with increasing altitude for high solar activity. [55] We now consider electron acceleration with energy below the vibrational barrier s lower boundary up to energy above the vibrational barrier s upper boundary. In this case, electrons with an energy at or below 1.6 ev must accelerate to an energy of 4 ev for a much shorter distance than the free path of these electrons. According to Gurevich et al. [2004], the length of the accelerating layer can be taken to be equal to 2000 Debye length. The caviton size is a =15 20 l De and the distance between cavitons is estimated to be d =50l De.Thel De value varies from 0.4 to 0.6 cm for T e =0.1eV=1161K and Figure 13. The n ev /n ee ratio calculated for low and high solar activities (thin and thick curves, respectively) at altitudes of 230, 250, 270, and 290 km (solid, dashed, dashed-dotted, and dotted curves, respectively). 3887